Download 7.2 Two-Variable Linear Systems

7.2 Two-Variable Linear
Systems
Elimination method
Solve for (x, y)
Given the System, I want to reduce the
number of variables. By multiplying both
sides of each equation by a number, we
can have opposite coefficients to add
together to eliminate a variable.
3 x  2 y  20
6 x  5 y  50
Solve for (x, y)
Given
3 x  2 y  20  23 x  2 y  20   6 x  4 y  40
6 x  5 y  50  16 x  5 y  50   6 x  5 y  50
 y  10
y  10
Solve for (x, y)
Given
3 x  2 y  20  23 x  2 y  20   6 x  4 y  40
6 x  5 y  50  16 x  5 y  50   6 x  5 y  50
 y  10
Now to find x replace y
with 10, in either equation
y  10
Solve for (x, y)
Given
3 x  2 y  20  23 x  2 y  20   6 x  4 y  40
6 x  5 y  50  16 x  5 y  50   6 x  5 y  50
 y  10
y  10
3 x  210   20
3 x  20  20
3x  0
x0
0,10 
Airplane Speed
An airplane flying into a headwind travels
the 1800-mile flying distance between
Pittsburgh, Pennsylvania and Phoenix,
Arizona in 3 hour hours and 36 minutes.
On the return flight, the distance is
traveled in 3 hours.
Find the airspeed of the plane and the
speed of the wind, assuming that both
remain constant.
Airplane Speed
Airplane travels the 1800-mile in 3 hour
hours and 36 minutes.
Return the same distance in 3 hours.
Find the airspeed, speed of the wind,
both constant. Write variable for Speeds
Airplane speed r
Wind speed w
Airplane Speed
Airplane travels the 1800-mile in 3 hour
hours and 36 minutes.
Return the same distance in 3 hours.
Airplane speed r
Wind speed w
 36 
r  w  3   1800
 60 
r  w (3)  1800
Airplane Speed
r  w  3 36   1800
 60 
r  w (3)  1800
1800
r  w 3.6  1800  r  w  
3.6
1800
r  w (3)  1800  r  w  
3
Airplane Speed
r  w  3 36   1800
 60 
r  w (3)  1800
r  w 3.6  1800  r  w   500
r  w (3)  1800  r  w   600
2r  1100
r  550
Airplane Speed
r  w   500
r  w   600
2r  1100
r  550
550  w  600
w  50
Homework
Page 495 -498
# 4, 16, 24, 32,
40, 48, 49, 63,
74, 80
Homework
Page 495 -498
# 12, 20, 28, 36,
44, 52, 67, 76,
82